Schaum's Outline of Probability, Third Edition

ISBN-13: 9781264258840

Media Type: Paperback

Publisher: McGraw Hill LLC

Publication Date: 11-12-2021

Pages: 320

Product Dimensions: 8.20(w) x 10.80(h) x 1.10(d)

Seymour Lipschutz, Ph.D., was on the mathematics faculty of Temple University and previously taught at the Polytechnic Institute of Brooklyn. He was also a visiting professor in the Computer Science Department of Brooklyn College. His work in the Schaum's Outline series includes Beginning Linear Algebra, Discrete Mathematics Fourth Edition, and Linear Algebra, Sixth Edition.Marc Lipson, Ph.D., is on the faculty of the University of Virginia. Previously, he taught at the University of Georgia, Northeastern University, and Boston University. He is the coauthor of Schaum’s Outline of Discrete Mathematics, Fourth Edition. Marc Lipson, Ph.D. (Philadelphia, PA), is on the mathematical faculty of the University of Georgia. He is co-author of Schaum's Outline of Discrete Mathematics.

Table of Contents

Chapter 1 Set Theory 1

1.1 Introduction.

1.2 Sets and Elements, Subsets.

1.3 Venn Diagrams.

1.4 Set Operations.

1.5 Finite and Countable Sets.

1.6 Counting Elements in Finite Sets, Inclusion-Exclusion Principle.

1.7 Products Sets.

1.8 Classes of Sets, Power Sets, Partitions.

1.9 Mathematical Induction.

Chapter 2 Techniques of Counting 32

2.1 Introduction.

2.2 Basic Counting Principles.

2.3 Factorial Notation.

2.4 Binomial Coefficients.

2.5 Permutations.

2.6 Combinations.

2.7 Tree Diagrams.

Chapter 3 Introduction to Probability 59

3.1 Introduction.

3.2 Sample Space and Events.

3.3 Axioms of Probability.

3.4 Finite Probability Spaces.

3.5 Infinite Sample Spaces.

3.6 Classical Birthday Problem.

Chapter 4 Conditional Probability and Independence 85

4.1 Introduction.

4.2 Conditional Probability.

4.3 Finite Stochastic and Tree Diagrams.

4.4 Partitions, Total Probability, and Bayes' Formula.

4.5 Independent Events.

4.6 Independent Repeated Trials.

Chapter 5 Random Variables 119

5.1 Introduction.

5.2 Random Variables.

5.3 Probability Distribution of a Finite Random Variable.

5.4 Expectation of a Finite Random Variable.

5.5 Variance and Standard Deviation.

5.6 Joint Distribution of Random Variables.

5.7 Independent Random Variables.

5.8 Functions of a Random Variable.

5.9 Discrete Random Variables in General.

5.10 Continuous Random Variables.

5.11 Cumulative Distribution Function.

5.12 Chebyshev's Inequality and the Law of Large Numbers.

Chapter 6 Random Variable Models 177

6.1 Introduction.

6.2 Bernoulli Trials, Binomial Distribution.

6.3 Normal Distribution.

6.4 Evaluating Normal Probabilities.

6.5 Normal Approximation of the Binomial Distribution.

6.6 Calculations of Binomial Probabilities Using the Normal Approximation.

6.7 Poisson Distribution.

6.8 Miscellaneous Discrete Random Variables.

6.9 Miscellaneous Continuous Random Variables.

Chapter 7 Markov Chains 224

7.1 Introduction.

7.2 Vectors and Matrices.

7.3 Probability Vectors and Stochastic Matrices.

7.4 Transition Matrix of a Markov Process.

7.5 State Distributions.

7.6 Regular Markov Processes and Stationary State Distributions.

Appendix A Descriptive Statistics 245

A.1 Introduction.

A.2 Frequency Tables, Histograms.

A.3 Measures of Central Tendency; Mean and Median.

A.4 Measures of Dispersion: Variance and Standard Deviation.

A.5 Bivariate Data, Scatterplots, Correlation Coefficients.

A.6 Methods of Least Squares, Regression Line, Curve Fitting.

Appendix B Chi-Square Distribution 282

B.1 Introduction.

B.2 Goodness of Fit, Null Hypothesis, Critical Values.

B.3 Goodness of Fit for Uniform and Prior Distributions.

B.4 Goodness of Fit for Binomial Distribution.

B.5 Goodness of Fit for Normal Distribution.

B.6 Chi-Square Test for Independence.

B.7 Chi-Square Test for Homogeneity.

Index 309